It is well known that in conventional three dimensional (3D) Hermitian two band models, the intersections between the energy bands are generically given by points. The typical example are Weyl semimetals, where these singular points can be effectively described as Weyl fermions in the low energy regime. By explicitly imposing discrete symmetries or fine-tuning, the intersection can form higher- dimensional nodal structures, e.g. nodal lines. By instead considering dissipative contributions to such a system, the degeneracies will generically take the form of closed 1D curves, consisting of exceptional points, i.e. points where the Hamiltonian becomes defective. By constructing the Hamiltonian in a particular way, the 1D exceptional curves can host non-trivial topology, i.e. they can form links or knots in the Brillouin zone. In stark contrast to line nodes occurring in Hermitian systems, which inevitably rely on discrete symmetries or fine tuning, the exceptional knots are generically stable towards any small perturbation. In further contrast to point singularities and unknotted circles, the topology of knots cannot be characterized by usual integer valued invariants. Instead, the complexity of the knottedness is captured by polynomial type invariants, making the physical classification and interpretation of these system challenging. To this end, the study of knotted nodal band structures naturally brings two different aspects of topology together – mathematical knot theory on the one hand, and the physical theory of topological phases on the other hand. This licentiate thesis focuses on providing the necessary theoretical background to understand the two accompanying publications entitled Knotted non-Hermitian metals, written by Johan Carlström, together with the author of this thesis, Jan Carl Budich and Emil J. Bergholtz, published in Physical Review B on April 24 2019, and Hyperbolic nodal band structures and knot invariants, written by the author of this thesis, together with Lukas Rødland, Gregory Arone, Jan Carl Budich and Emil J. Bergholtz, published in SciPost Physics August 8 2019. An introduction to gapless topological phases in the Hermitian regime, focusing on Weyl semimetals, their classification and surface states, is provided. Then, the light is brought to non-Hermitian operators and the differences from their conventional Hermitian counterpart, such as the two different set of eigenvectors bi-orthogonal to each other, exceptional eigenvalue degeneracies and some of their consequences, are explained. Afterwards, these operators are applied to dissipative physical system, and some of the striking differences from the conventional Hermitian systems are highlighted, the main focus being the possibly non-trivial topology of the 1D exceptional eigenvalue degeneracies. In order to be somewhat self contained, a brief conceptual introduction to the utilized concepts of knot theory is given, and lastly, further research directions and possible experimental realization of the considered systems are discussed.

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The study of the properties of magnetic materials is of primary importance in the development of newtechnologies. In this project, we aim to investigate the symmetries of some of the relevant properties ofa cobalt and platinum alloy that emerge from the symmetry of the crystal structure of the alloy. Morespecifically, our goal is to calculate the magnetocrystalline anisotropy energy (MAE) for various orientations of the magnetization. The MAE is computed through the implementation of density functionaltheory (DFT) via the open-source package OpenMX.The project consists of three main parts: Study on the convergence of the total energy of the systemas a function of some relevant parameters, computation of the energy, the spin magnetic moment andthe orbital magnetic moment as a function of the orientation of the magnetization, and a calculation ofthe magnetocrystalline anisotropy energy of the studied alloy.The studied system is an ordered compound of cobalt and platinum, with a tetragonal crystal structure.The easy axis of magnetization was found to be along the c-axis of the crystal, and defined accordinglytowards the z-axis in cartesian coordinates. The compound exhibits angular symmetry for the energy,the spin and orbital magnetic moments and the MAE, with a minimum energy along the easy axis ofmagnetization and a maximum at spherical angles θ=90◦ and ϕ=45◦. Looking at the plots for the MAE,this maximum can be interpreted as an energy barrier that must be surpassed in order to invert thedirection of the magnetization. Using an expression of the MAE in spherical angles, theoretical valuesfor the anisotropy constants K1, K2 and K3 are determined. / Computational Study of the Magnetocrystalline Anisotropy Energy of Ordered CoPt

This thesis aims to study the nonlinear electrical transport response of monolayer and bilayer graphene systems under the influence of different lattice deformations (strain). Broken inversion and rotation symmetries can generate a second-order transverse current response called the nonlinear Hall effect in the presence of time-reversal symmetry. The nonlinear Hall currents are proportional to the Berry curvature dipole (BCD), a quantity proportional to an intrinsic topological quantity known as the Berry curvature. We investigate homo-strain and hetero-strain in bilayer graphene, in which the two carbon layers are deformed symmetrically and asymmetrically respectively. Our numerical results show that bilayer graphene systems give a larger BCD, up to an order of magnitude using homo-strain and up to two orders of magnitude using heterostrain, when compared to monolayer graphene for the same strain due to larger Berry curvature and density of states. Furthermore, we obtain a large BCD in bilayer graphene under hetero-strain, which breaks both the inversion and three-fold rotational symmetries. Based on an effective k · p analysis, it is necessary to consider higher-order corrections, that are linear in momentum qj and strain uij, in the velocity renormalization of the Dirac fermions to obtain a finite Berry curvature induced by hetero-strain. Larger BCD and the implication of hetero-strain make bilayer graphene a better candidate for practical applications such as detecting terahertz radiation. The result of this thesis motivates the investigation of hetero-strain in twisted bilayer graphene, a hot topic in condensed matter physics. In particular, the impact of strain-induced velocity renormalization is not explored systematically in the literature, which can be a subject of future study.

High-entropy alloys (HEA) is a class of materials consisting of multiple principal elements that often crystallize in simple lattices such as body-centered cubic, face-centered cubic and hexagonal close-packed structures. Many HEAsexhibit exceptional mechanical properties, e.g., impact toughness and ductility at cryogenic temperatures and high temperature creep strength. Out of the known magnetic HEAs, the Cantor alloy, consisting of equalparts of Co, Cr, Fe, Mn, and Ni, is by far the most investigated. The influenceof magnetism on the stability and mechanical properties for these alloys isintricate and very interesting for that reason. The concentration dependencein this alloy is, however, fairly unexplored and it would be beneficial if onecould avoid including critical elements such as Co. As such, the purpose of this work was to find a suitable replacement forCo in the Cantor alloy. Using density functional theory, the Co-concentrationwas investigated by replacing Co with the other constituent elements in different ways. It was discovered that the most energetically stable configurations,with magnetic and structural properties similar to the equiatomic alloy, werefound in the body-centered cubic phase when replacing Co with Fe.

The purpose of this study is to approximate the local density of states(LDOS) for a metal block by solving the Schrödinger equation in an efficient way. To make the code more effective different methods were implemented, for example trying to parallelize the process and to run the code solely on a GPU (Graphic Processing Unit). The conclusion that was drawn was that running the code in parallel over the different orbitals on a multicore central processing unit (CPU) is faster and thusmore efficient than running it in sequential order. Running the calculations on a GPU was determined to be slower because of inefficient use of its bandwidth due to individual indexing in matrices and vectors. Further tests using block versions of the same algorithm on GPUs couldbe of interest because of better use of the available bandwidth. These tests were not done due to time constraints.

At the division of Material Physics at KTH an angle resolved photoemission spectrometer (ARPES) is being built. This system uses a pulsed laser to create ultraviolet light through higher harmonic generation. The laser has a high output effect which puts the optical components of the system under a large heat load. This thesis investigates the use of silicon carbide (SiC) as a possible material for use in the system. A diffraction grating is modelled and then processed by use of photolithography and plasma etching. This is then characterized by different methods, finally in its working environment. It is concluded that silicon carbide is a plausible material for use in the ARPES system. / Vid avdelningen för materialfysik vid KTH håller en laserbaserad vinkelupplöst fotoemissionsspektrometer på att byggas upp. Denna använder ultraviolett ljus för att excitera fotoelektroner som sedan detekteras genom time of flight. Ljuskällan som ger UV-fotonerna är en pulsad laser som ger en hög effekt, vilket ställer krav på att alla optiska komponenter i systemet skall klara en hög värmelast. I detta examensarbete undersöks om kiselkarbid (SiC) uppfyller dessa krav. Modellering av ett diffraktionsgitter görs, och resultatet av detta ger vägledning under processningen av gittret. Gittret tillverkas med hjälp av fotolitografi och plasmaetsning av en kiselkarbidwafer. Denna karakteriseras sedan med olika metoder och finns fungera bra för sitt ändamål.

For the high-power (HP) electronic applications the existing Si-based devices have reached the performance limits governed by the material properties. Hence the device innovation itself is unable to enhance the overall performance. GaN, a semiconductor with wide bandgap, high critical breakdown field, and high electronic saturation velocity is regarded as an alternative of Si. The material properties of GaN make it very suitable for fast-switching HP electronic devices and contribute to the fast growing of GaN technology. The state-of-the-art GaN devices operating up to 650 V have recently become commercially available. Further goal is to reach higher breakdown voltage which can be done via device engineering and material growth optimization. AlxGa1−xN is an ultrawide-bandgap (UWBG) semiconductor which is considered as a natural choice for next generation in the development of GaN-based HP electronic devices. This material attracts particular interest due to the possibility for bandgap tuning from 3.4 eV to 6 eV which allows nonlinear increase of avalanche breakdown field. Furthermore, both n- and p-type conductivity can be achieved on this material permitting variety of device design with reduced energy losses during operation. β−Ga2O3 is also a promising material for HP electronics because of its ultra-wide bandgap (4.8 eV) and a huge value of Baliga’s figure of merit (FOM) exceeding by far that of GaN. More interesting feature making this material attractive is the availability of low-cost natural substrates, and then the possibility to obtain high crystal quality of device structures. For the HP electronic devices thermal conductivity is one of the key parameters determining the device’s performance. The initial studies have shown that the thermal conductivity of AlxGa1−xN and β−Ga2O3 is quite low comparing with that of GaN. This is one of the biggest challenges slowing the development of these materials for HP device applications. Nevertheless, AlxGa1−xN- and β−Ga2O3-based field-effect transistors and Schottky-barrier diodes have been demonstrated showing performances superior to that of GaN. To optimize and maintain good performance and reliability, heat generated in the device active regions has to be effectively dissipated. Therefore the thermal conductivity of the materials in the device structures needs to be systematically studied and accurately determined. This information is critically important for the thermal management of the devices. Transient thermoreflectance (TTR) is a contactless nondestructive method for measuring of the thermal conductivity of materials. TTR, which is based on a pump-probe technique, has shown its potential in evaluation of the thermal conductivity in bulk crystals as well as in thin layers in hetero-epitaxial structures. The method requires an analysis of experimental data based on the fit of thermoreflectance transients with the solution of the one-dimensional heat transport equations by a least-square minimization of the fitting parameters. Such a procedure allows to extract not only the thermal conductivity of the constituent materials in the structures, but also the thermal boundary resistance at different hetero-interfaces. The main research results of the graduate studies presented in this licentiate thesis are summarized in three scientific papers. Paper I. In this paper thermal conductivity of β−Ga2O3 and high Al-content AlxGa1−xN thin layers was studied. For β−Ga2O3 the the effects of Sn doping and phonon-bondary scattering on the reduction of thermal conductivity were discussed. For the AlxGa1−xN we studied the effect of Al-Ga alloying which gives rise to phonon-alloy scattering. It was found that this scattering process accounts for low thermal conductivity of this material. Finally, a comparison for the thermal conductivity of the two materials was made. Paper II. In this paper the effect of layer thickness on the thermal conductivity of AlxGa1−xN layers grown by HVPE were investigated. Due to Al alloying the thermal conductivity of this material is degraded and reduced by more than one order of magnitude. On top of that we also observed further reduction of thermal conductivity when the layer thickness goes thinner. The mechanism of this phenomenon has been revealed by studying the phonon transport properties in bulk crystal and thin layer. Paper III. This study emphasizes the role of defects in GaN and AlxGa1−xN to the thermal conductivity of these materials. The dislocations, impurities, free carries, and random alloying have been separately studied and discussed. Thermal conductivity of samples containing these defects with various concentrations was measured and the results were interpreted by a theoretical model based on relaxation time approximation (RTA). / <p>Additional funding agencies: the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University, Faculty Grant SFO Mat LiU No. 2009 − 00971</p>

Group-III nitride materials, gallium nitride (GaN), aluminum nitride (AlN) and indium nitride (InN) have direct band gaps with band gap energies ranging from the infrared (InN) to the ultraviolet (GaN) and to the deep ultraviolet (AlN) wavelengths and covering the entire spectral range from 0.7 eV to 6.2 eV upon alloying. The invention of the GaN-based blue LEDs, for which the Nobel prize in Physics was awarded in 2014, has opened up avenues for exploration of IIINitride material and device technologies and has inspired generations of researchers in the semiconductor field. Group-III nitrides have also been demonstrated to be among the most promising semiconductors for next generation of efficient high-power, high-temperature and high-frequency electronic devices. The need to build a sustainable and efficient energy system motivates the development of vertical GaN transistors and diodes for applications with power ratings of 50-150 kW, e.g., in electric vehicles and industrial inverters. The key is to grow GaN layers with low concentration of defects (impurities and dislocations), which enables an expansion in both voltage and current ratings and reduction of cost. Despite intense investigations and impressive advances in the field, defects are still a major problem hindering exploiting the full potential of GaN in power electronics. This Licentiate thesis focuses on the development of two different epitaxial approaches in MOCVD for reducing dislocation densities in GaN with controlled doping for power device applications: i) growth of planar GaN layers trough NWs reformation, which can be further exploited as templates for a subsequent growth of thick drift layers and ii) homoepitaxial GaN growth. Special attention is put on understanding homoepitaxial growth under different nucleation schemes and thermal stability of GaN. We have established conditions in homoepitaxy to deliver state-of-the-art GaN material with low impurity levels combined with a reasonable growth rate suitable for growth of thick drift layers. The results are summarized in two papers: In Paper I we investigate GaN layers with different thicknesses on reformed GaN NW templates and highlight this approach as an alternative to the expensive GaN HVPE substrates. The sapphire used as a substrate limits to some extent the reduction of threading dislocations, however, the resulting GaN material presents smooth surfaces and thermal conductivity close to the bulk value, which suggests the potential of this approach to be integrated in GaN development as an active material for power devices on various substrates. In Paper II extensive study of homoepitaxial GaN growth by hot-wall MOCVD is presented together with results on the thermal stability of GaN under typical conditions used in our growth reactor. Understanding the evolution of GaN surface under different gas compositions and temperatures allows us to predict optimum homoepitaxial conditions. Analysis in the framework of Ga supersaturation of epilayers simultaneously grown on GaN templates and on GaN HVPE substrates reveals that residual strain and screw dislocation densities affect GaN nucleation and growth and lead to distinctively different morphologies on GaN templates and native substrates, respectively. The established comprehensive picture provides guidance for designing strategies for growth conditions optimization in homoepitaxy. We demonstrate homoepitaxial GaN-on-GaN grown under optimum growth conditions with state-of-the-art smooth surface with an rms value of 0.021 nm and an average TDD of 1.4·106 cm-2 which provide good basis for augmenting power device structures.Future work will be focused on GaN NWs reformation on different substrates, p- and n-type doping of homoepitaxial GaN with impurity control and the fabrication of pn power diode device structures for further processing and assessment by C3NiT partners. / <p>Funding agencies: The Swedish Research Council (VR) under Grant No. 2016-00889, The Swedish Governmental Agency for Innovation Systems (VINNOVA) under the Competence Center Program, Grant No. 2016-05190, The Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University, Faculty Grant SFO Mat LiU No.2009-00971, The Swedish Foundation for Strategic Research (SSF), under Grant No. EM16-0024</p>

The devolopment of group-III nitride semiconductor technology continues to expand rapidly over the last two decades. The indium nitride (InN), gallium nitride (GaN) and aluminum nitride (AlN) compounds and their alloys are direct bandgap semiconductors with a wide bandgap range, spanning from infrared(IR) to deep-ultraviolet (UV), enabling their utilization in optoelectronic industry. The GaN-based light-emitting diode (LED) is already the commercial solution for efficient and energy saving lighting. Additionally, the physical properties of these materials such as the high critical electric field, the high saturation carrier velocity and the high thermal conductivity, make them promising candidates for replacing silicon (Si), and other wide-bandgap semiconductors such as silicon carbide (SiC) in power devices. More importantly, the polarization-induced two-dimensional electron gas (2DEG), forming at the interfaces of these semiconductors, led to the fabrication of the GaN-based high electron mobility transistor (HEMT). This device is suitable for high power (HP) switching, power amplifiers and high frequency (HF) applications in the millimeter-wave range up to THz frequencies. As such, HEMTs are suitable for 5G communication systems, radars, satellites and a plethora of other related applications. Achieving the efficient GaN blue LED (Nobel Prize in Physics 2014), came as a result of (partially) solving several material issues of which, p-type GaN was of crucial importance. Since 1992, a lot of effort is being dedicated on the understanding and overcoming of the limitations hindering efficient p-type conductivity and low hole mobility in metal-organic chemical vapor deposition (MOCVD) grown p-GaN. The limitations arise from the fact that magnesium (Mg) is the only efficient p-type dopant for GaN so far and only a very small percentage ∼2% of the incorporated Mg is active at room temperature. More limitations come from its solubility in GaN and the crystal quality deterioration and formation of inversion domains (IDs) at high doping levels. Free-hole concentrations in the low 1018 cm-3 range with mobilities at ∼10 cm2V-1s-1 demonstrate the state-of-art in MOCVD grown p-GaN, still leaving a wide window for improvement. Another intensively investigated topic is related to the aluminum gallium nitride (AlGaN)/GaN HEMTs. High electron density and mobility of the 2DEG in the range of 1013 cm-2 and ∼2400 cm2V-1s-1 respectively, are reported. Interface engineering, addition of interlayers and backbarriers are only some of the modifications introduced at the basic AlGaN/GaN HEMT structure in order to achieve the aforementioned values. Nevertheless, fundamental phenomena can still be revealed by special characterization techniques and provide a deeper understanding on the causal factors of theHEMT’s macroscopic properties. The main research results presented in this licentiate thesis are organized in three papers: In paper I we perform an in-depth investigation of the Mg-doped GaN growth by hot-wall MOCVD. We strive for exploiting any possible advantages of the hot-wall MOCVD on the growth of high-quality p-GaN relevant for use in HP devices. Additionally, we aim to gain a comprehensive understanding of the growth process and its limiting factors. The effects of growth conditions on the Mg, hydrogen (H) and carbon (C) incorporation in GaN are approached from the gallium (Ga)-supersaturation point of view. Control of the bis(cyclopentadienyl) magnesium (Cp2Mg)/trimethylgallium(TMGa) ratio, the V/III ratio and the growth temperature, resulted in high quality p-GaN growth on AlN/4H-SiC templates, showing state-of-the-art electrical properties. In paper II, we manage to increase the free-hole concentrations in as-grown GaN:Mg in two different ways, either by growing the GaN:Mg layer on a GaN/AlN/4H-SiC template, or by modifying the gas environment of the growth. It is shown that using a GaN/AlN/4H-SiC template results in higher carrier concentration and large improvement of the as-grown p-GaN resistivity. More importantly, the high amount of hydrogen (H2) flow during GaN:Mg growth, results in higher amount of non-passivated Mg in the as-grown layers allowing for high free-hole concentration and significantly lower resistivity in the as-grown p-GaN. Paper III focuses on the effect of aluminum (Al)-content variation in the barrier layer of AlGaN/GaN HEMTs. The THz-optical Hall effect (OHE) measurements revealed a peak of the 2DEG mobility followed by a decrease above certain value of Al%. We correlate this effect with the electron effective mass (meff) variation and draw conclusions about the mobility limiting mechanisms. In the low-Al regime, the mobility decreases because of the increase in meff while, in the high-Al regime, the mobility is limited by the lower carrier scattering time. / <p>Funding agencies: The Swedish Governmental Agency for Innovation Systems (VINNOVA) under the Competence Center Program Grant No.2016−05190, Linköping University, Chalmers University of technology, Ericsson, Epiluvac, FMV, Gotmic, Hexagem, Hitachi Energy, On Semiconductor, Saab, SweGaN, UMS, the Swedish Research Council VR under Award No. 2016 − 00889, the Swedish Foundation for Strategic Research under Grants No. RIF14 − 055 and No. EM16 − 0024, and the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University, Faculty Grant SFO Mat LiU No.2009 − 00971.</p>